Annals of Probability

Kolmogorov's test for super-Brownian motion

Jean-Stéphane Dhersin and Jean-François Le Gall

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We prove a Kolmogorov test for super-Brownian motion started at the Dirac mass at the origin. More precisely, we determine the functions $g$ such that for all $t$ small enough, the support of the process at time $t$ will be contained in the ball of radius $g(t)$ centered at 0. As a consequence, we get a necessary and sufficient condition for the existence in certain space-time domains of a solution of the associated semilinear partial differential equation that blows up at the origin.

Article information

Ann. Probab., Volume 26, Number 3 (1998), 1041-1056.

First available in Project Euclid: 31 May 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G17: Sample path properties
Secondary: 60G57: Random measures

Super-Brownian motion Brownian snake Kolmogorov test exit measure semilinear partial differential equation


Dhersin, Jean-Stéphane; Le Gall, Jean-François. Kolmogorov's test for super-Brownian motion. Ann. Probab. 26 (1998), no. 3, 1041--1056. doi:10.1214/aop/1022855744.

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